To determine the spatial extension of a source, an extended source model has to be used in the model definition file of the source of interest. In the example below, a RadialGaussian model is used for the source Src001 to model the spatial morphology of the source by an axisymmetric Gaussian profile with the Gaussian width sigma as free parameter. Note that at the same time the source type has been set to ExtendedSource.
<source name="Src001" type="ExtendedSource">
<spectrum type="PowerLaw">
<parameter name="Prefactor" value="1" scale="5.7e-18" min="0" free="1" />
<parameter name="Index" value="1" scale="-2.48" min="-5" max="5" free="1" />
<parameter name="PivotEnergy" value="1" scale="300000" free="0" />
</spectrum>
<spatialModel type="RadialGaussian">
<parameter name="RA" scale="1.0" value="266.4240" min="-360" max="360" free="1"/>
<parameter name="DEC" scale="1.0" value="-29.0049" min="-90" max="90" free="1"/>
<parameter name="Sigma" scale="1.0" value="0.05" min="0.001" max="10" free="1"/>
</spatialModel>
</source>
Running ctlike using the modified model definition file will then fit the Gaussian width of Src001. The results can be seen in the log file and will also be written into the output model definition file.
For illustration, an excerpt of the ctlike log file is shown below. The Gaussian width of Src001 has been fitted to 0.0218 +/- 0.0006 degrees.
2017-03-04T17:44:06: === GModelSky ===
2017-03-04T17:44:06: Name ......................: Src001
2017-03-04T17:44:06: Instruments ...............: all
2017-03-04T17:44:06: Instrument scale factors ..: unity
2017-03-04T17:44:06: Observation identifiers ...: all
2017-03-04T17:44:06: Model type ................: ExtendedSource
2017-03-04T17:44:06: Model components ..........: "RadialGaussian" * "PowerLaw" * "Constant"
2017-03-04T17:44:06: Number of parameters ......: 7
2017-03-04T17:44:06: Number of spatial par's ...: 3
2017-03-04T17:44:06: RA .......................: 266.416716505268 +/- 0.000753191747203773 [-360,360] deg (free,scale=1)
2017-03-04T17:44:06: DEC ......................: -29.0044104159472 +/- 0.000655420291471696 [-90,90] deg (free,scale=1)
2017-03-04T17:44:06: Sigma ....................: 0.02183871432113 +/- 0.000636651479386333 [0.001,10] deg (free,scale=1)
2017-03-04T17:44:06: Number of spectral par's ..: 3
2017-03-04T17:44:06: Prefactor ................: 4.85894838349519e-17 +/- 7.40461052122477e-19 [0,infty[ ph/cm2/s/MeV (free,scale=5.7e-18,gradient)
2017-03-04T17:44:06: Index ....................: -2.29168205335762 +/- 0.00909936860902909 [10,-10] (free,scale=-2.48,gradient)
2017-03-04T17:44:06: PivotEnergy ..............: 300000 MeV (fixed,scale=300000,gradient)
2017-03-04T17:44:06: Number of temporal par's ..: 1
2017-03-04T17:44:06: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
Warning
The errors returned by ctlike are purely statistical. In addition there are systematic uncertainties, such as for example the limits in the knowledge of the point spread function. It remains to be seen whether CTA will be able to reliably determine source extents as small as 0.02 degrees.